Abstract: In this paper, we will compute asymptotically the eigenfrequencies for the in-plane vibrations of an Euler-Bernoulli beam system with dissipative joints, which allow the beams to be curved into an arc of a circle. This enhances the author's previous result for structures involving straight beams, given in his preprint ``Eigenfrequencies of the non-collinearly coupled Euler-Bernoulli beam system with dissipative joints". Matrix techniques are used to combine asymptotic analysis with a form of the wave propagation method.